A boundary wall around a rectangular plot is constructed at a total cost of Rs. 46000 at the rate of Rs. 200 per metre. What is the area of the plot if the respective ratio between the breadth and the length of the plot is 10 : 13 ? (in sq. metre)

Answer: Option B

Total cost to construct a boundary wall around a rectangular plot = Rs. 46000
Rate of construction per metre = Rs. 200
Perimeter of rectangular plot = $$\frac{46000}{200}$$   = 230 m
Let the length and breadth of rectangular plot be 13x metre and 10x metre respectively
$$\begin{array}{rl}& \therefore 2\left(13x+10x\right)=230\\ & \Rightarrow 2\times 23x=230\\ & \Rightarrow x=\frac{230}{2\times 23}\\ & \Rightarrow x=5\end{array}$$
∴ Length = 13 × 5 = 65 cm
Breadth = 10 × 5 = 50 m
∴ Area of plot = 65 × 50 = 3250 sq. m²